Offered load estimation in random access multipacket perception systems using the expectation-maximization algorithm

We present a computationally efficient method of evaluating the probability of multiple correct packet reception in coded synchronous frequency-hopped spread-spectrum (FHSS) networks. We show that the approximation using the independent receiver operation assumption (IROA), which has been frequently employed in the literature without rigorous validation, produces reasonable results in most network load conditions when compared to the exact computations derived from our proposed method. Specifically, the expected value of the absolute error was in the range of 0.0055%-18.21% in the investigated scenarios.

Multiple packet reception (MPR) is becoming a viable reality for wireless random access protocols thanks to advances in the physical layer and new coding techniques. In the simplest $K$ -MPR model, a receiver can resolve up to $K\geq 1$ parallel transmissions. We extend the classical analysis of pure and slotted ALOHA to $K$ -MPR devices with arbitrary degree $K$ for fixed and variable packet size. Through a parsimonious modeling approach, we derive relatively simple analytical expressions. In this way, we gain insight and quantitative understanding on the fundamental tradeoffs between pure and slotted ALOHA and on the scaling of maximum achievable throughput with $K$ .

In this paper, we propose an analytical approach for evaluating the performance of finite-user slotted Aloha in wireless networks with multiple packet reception and random traffic. We derive the exact values of the throughput, the average system size, the packet blocking probability, and the average system delay. Our analysis is based on probability theory. We show that our numerical results are identical to simulation results.

A modified bit-map-assisted dynamic queue (BMDQ) protocol is presented for wireless slotted systems with multiple packet reception (MPR) capability and finite user-buffers. As in our BMDQ protocol (Xin Wang and Tugnait, J.K., Proc. Joint Intern. Conf. Wireless LANs & Home Networks and Networking, p.549-60, 2002), in the proposed protocol, the traffic in the channel is viewed as a flow of transmission periods (TP). Each TP has a bit-map (BM) slot at the beginning followed by a data transmission period (DP). In the BMDQ protocol the BM slot is reserved for user detection so that accurate knowledge of the active user set (AUS) can be acquired and in any given TP, each active user is allowed to transmit only one data packet. In the proposed modified BMDQ protocol, the active users are allowed to transmit all data packets in their finite buffer. An active user with more than one packet in its buffer is modeled as several different active pseudo-users. In the BM slot, each user transmits information about the number of data packets in its buffer. Then, according to the number of the active pseudo-users and the channel MPR capability, the protocol attempts to minimize the expected duration of the DP in the same way as the BMDQ protocol. Simulation comparison of the performance of the proposed modified BMDQ protocol with that of the original BMDQ protocol is presented.

A mobile packet communication with a chained isolated radio zone network system is proposed that provides nonrealtime media services including voice messages, images, and navigation information, etc., to terminals in cars. In this system, microradio zones are located along a road to establish the communication between a radio base station and a terminal by using packets in a common format. A terminal receives the signal by the paging channel covering a wide area and transmits packets sequentially when a terminal passes radio zones. Therefore, only three radio frequencies, inbound, outbound, and paging channels, are enough and location registration of all terminals is not necessary to realize the proposed system. When transmission and reception of multiple packets is not completed in a single radio zone, it can be done in other radio zones. Since every terminal has a different staying time in each radio zone, the relationship between staying time and throughput, and the relationship between staying time and message transmission ratio are examined and evaluated by the simulation.

Multi-Packet Reception (MPR) enables simultaneous receptions from different transmitters to a single receiver, which has been demonstrated to bring capacity improvement in wireless network. However, MPR does not improve the transmission capability of intermediate relay nodes in a multi-hop routing and thus these nodes may become the bottlenecks for increasing throughput despite of great reception capability. We investigate the scheduling for multi-hop routing with MPR to improve the network throughput under multiple data flows. We formulate the optimization problem under K-MPR model and analyze the performance upper bound with ideal scheduling. We propose a distributed scheduling scheme based on a k-Connected k-Dominating Set backbone to eliminate bottleneck effects on intermediate relay nodes as to enhance the network throughput. We show the effectiveness of our scheme by comparing its performance with the upper bound and node-disjoint routing.

We present an approach that takes advantage of multi-packet reception (MPR) to reduce the negative effects of multiple access interference and therefore increase the capacity of an ad hoc network. We analyze the performance upper bound of joint routing and scheduling for ad hoc networks that embrace interference by using MPR. We formulate the optimization problem under a deterministic model and seek to maximize the aggregate network throughput subject to minimum rate requirements. We then propose a polynomial-time heuristic algorithm aimed at approximating the optimal solution to the joint routing and channel access problem under MPR. We show the effectiveness of our heuristic algorithm by comparing its performance with the upper bound.

This paper provides a unified framework to study the performance of successive interference cancellation (SIC) in wireless networks with arbitrary fading distribution and powerlaw path loss. An analytical characterization of the performance of SIC is given as a function of different system parameters. The results suggest that the marginal benefit of enabling the receiver to successively decode k users diminishes very fast with k, especially in networks of high dimensions and small path loss exponent. On the other hand, SIC is highly beneficial when the users are clustered around the receiver and/or very low-rate codes are used. In addition, with multiple packet reception, a lower per-user information rate always results in higher aggregate throughput in interference-limited networks. In contrast, there exists a positive optimal per-user rate that maximizes the aggregate throughput in noisy networks. The analytical results serve as useful tools to understand the potential gain of SIC in heterogeneous cellular networks (HCNs). Using these tools, this paper quantifies the gain of SIC on the coverage probability in HCNs with nonaccessible base stations. An interesting observation is that, for contemporary wireless systems (e.g., LTE and WiFi), most of the gain of SIC is achieved by canceling a single interferer.

This paper concerns the cross-layer design between physical layer and MAC (multiple access control) layer in asynchronous wireless random access network. The proposed cross-layer design consists of two parts: a MPR (Multiple Packet Reception) physical layer and a collision- aware MAC layer. In the physical layer design, different spreading codes are assigned to packets according to their frame types at the transmitter, and at the receiver, an enhanced synchronization method and MUD (Multi-user Detection) are utilized to synchronize the collided packets and recover packets. In order to reduce the computational complexity of the receiver, interference cancellation is performed at the receiver by utilizing the known preamble and the partially known frame header information. In the MAC layer design, collisions are divided into different types according to frame types and packet arrival time, and different operations are developed for different collision types to tactically access the channel. Simulation results show that the proposed cross-layer design can significantly improve the network throughput and reduce the transmission delay.

We present an approach that takes advantage of multi-packet reception (MPR) to reduce the negative effects of multiple access interference and therefore increase the capacity of an ad hoc network. We analyze the performance upper bound of joint routing and scheduling for ad hoc networks that embrace interference by using MPR. We formulate the optimization problem under a deterministic model and seek to maximize the aggregate network throughput subject to minimum rate requirements. We then propose a polynomial-time heuristic algorithm aimed at approximating the optimal solution to the joint routing and channel access problem under MPR. We show the effectiveness of our heuristic algorithm by comparing its performance with the upper bound.

Objective: Data being missed is an unavoidable problem in cohort studies. This paper compares the imputation effect of eight common missing data imputation methods involved in cutting longitudinal data through simulation study to provide a valuable reference for the treatment of missing data in longitudinal studies. Methods: The simulation study is based on R language software and generates missing longitudinal data by the Monte Carlo method. By comparing the average absolute deviation, average relative deviation, and TypeⅠerror from the regression analysis of different imputation methods, the imputation effect of varying imputation methods on missing longitudinal data and the influence on subsequent multivariate analysis are evaluated. Results: The mean imputation, k nearest neighbor (KNN), regression imputation, and random forest all have a similar imputation effect, which is also steady. However, the hot deck is inferior to the above imputation methods. K-means clustering and expectation maximization (EM) algorithm are among the worst and unstable. Mean imputation, EM algorithm, random forest, KNN, and regression imputation can control TypeⅠerror. Still, multiple imputations, hot deck, and K-means clustering cannot effectively manage the TypeⅠerror. Conclusions: For missing data in longitudinal studies, mean imputation, KNN, regression imputation, and random forest can be used as better imputation methods under the mechanism of missing at random. When the missing ratio is not too large, multiple imputations and hot deck can also perform well, but K-means clustering and EM algorithm are not recommended.

Joint modeling of survival and longitudinal data has been studied extensively in the recent literature. The likelihood approach is one of the most popular estimation methods employed within the joint modeling framework. Typically, the parameters are estimated using maximum likelihood, with computation performed by the expectation maximization (EM) algorithm. However, one drawback of this approach is that standard error (SE) estimates are not automatically produced when using the EM algorithm. Many different procedures have been proposed to obtain the asymptotic covariance matrix for the parameters when the number of parameters is typically small. In the joint modeling context, however, there may be an infinite-dimensional parameter, the baseline hazard function, which greatly complicates the problem, so that the existing methods cannot be readily applied. The profile likelihood and the bootstrap methods overcome the difficulty to some extent; however, they can be computationally intensive. In this paper, we propose two new methods for SE estimation using the EM algorithm that allow for more efficient computation of the SE of a subset of parametric components in a semiparametric or high-dimensional parametric model. The precision and computation time are evaluated through a thorough simulation study. We conclude with an application of our SE estimation method to analyze an HIV clinical trial dataset.

Abstract. An expectation maximization (EM) algorithm is proposed to find fibre length distributions in standing trees. The available data come from cylindric wood samples (increment cores). The sample contains uncut fibres as well as fibres cut once or twice. The sample contains not only fibres, but also other cells, the so‐called ‘fines’. The lengths are measured by an automatic fibre‐analyser, which is not able to distinguish fines from fibres and cannot tell if a cell has been cut. The data thus come from a censored version of a mixture of the fine and fibre length distributions in the tree. The parameters of the length distributions are estimated by a stochastic version of the EM algorithm, and an estimate of the corresponding covariance matrix is derived. The method is applied to data from northern Sweden. A simulation study is also presented. The method works well for sample sizes commonly obtained from increment cores.

In this paper, we study the autoregressive (AR) model with normal inverse Gaussian (NIG) innovations. The NIG distribution is semi heavy-tailed and is helpful in capturing the extreme observations present in the data. The expectation-maximization (EM) algorithm is used to estimate the parameters of the considered AR(p) model. The efficacy of the estimation procedure is shown on the simulated data for AR(2) and AR(1) models. A comparative study is presented, where the classical estimation algorithms are also incorporated, namely, Yule-Walker and conditional least squares methods along with EM method for model parameter estimation. In simulation study, the maximum likelihood estimation (MLE) of NIG distribution by EM algorithm and iterative Newton-Raphson method are also compared. The real-life applications of the introduced model are demonstrated on the NASDAQ stock market index data and US gasoline price data. The studies show that AR(1) model with NIG residuals is good fit for financial data with extreme values as well as for gasoline price data.

An important property that any lifetime model should satisfy is scale invariance. In this paper, a new scale-invariant quasi-inverse Lindley (QIL) model is presented and studied. Its basic properties, including moments, quantiles, skewness, kurtosis, and Lorenz curve, have been investigated. In addition, the well-known dynamic reliability measures, such as failure rate (FR), reversed failure rate (RFR), mean residual life (MRL), mean inactivity time (MIT), quantile residual life (QRL), and quantile inactivity time (QIT) are discussed. The FR function considers the decreasing or upside-down bathtub-shaped, and the MRL and median residual lifetime may have a bathtub-shaped form. The parameters of the model are estimated by applying the maximum likelihood method and the expectation-maximization (EM) algorithm. The EM algorithm is an iterative method suitable for models with a latent variable, for example, when we have mixture or competing risk models. A simulation study is then conducted to examine the consistency and efficiency of the estimators and compare them. The simulation study shows that the EM approach provides a better estimation of the parameters. Finally, the proposed model is fitted to a reliability engineering data set along with some alternatives. The Akaike information criterion (AIC), Kolmogorov-Smirnov (K-S), Cramer-von Mises (CVM), and Anderson Darling (AD) statistics are used to compare the considered models.